Identify the infinite set among descriptions: Which of the following sets is infinite?
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A{x: x is a prime number, x is even}
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BSet of all rivers in India
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CSet of all concentric circles
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DNone of above
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EAll of these
Answer
Correct Answer: Set of all concentric circles
Explanation
Introduction / Context:An infinite set has no finite bound on its elements. Geometric constructions often yield infinite families (e.g., circles with the same center and varying radii).
Given Data / Assumptions:
- Even prime numbers: only {2} (finite)
- Rivers in one country: finite list
- Concentric circles about a fixed center: radius can vary over infinitely many positive values
Concept / Approach:Check whether there is a natural limiting count. Concentric circles admit unboundedly many radii.
Step-by-Step Solution:(a) = {2} → finite(b) Finite by geography(c) Infinite family by any distinct positive radius
Verification / Alternative check:Between any two radii, more radii exist (continuum), reinforcing infinitude.
Why Other Options Are Wrong:They are finite sets by definition or context.
Common Pitfalls:Misinterpreting 'even prime' as many primes; there is only one even prime.
Final Answer:Set of all concentric circles